Simplify the following expression: $ r = -2 - \dfrac{5k + 3}{5k} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5k}{5k}$ $ \dfrac{-2}{1} \times \dfrac{5k}{5k} = \dfrac{-10k}{5k} $ Therefore $ r = \dfrac{-10k}{5k} - \dfrac{5k + 3}{5k} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-10k - (5k + 3) }{5k} $ Distribute the negative sign: $r = \dfrac{-10k - 5k - 3}{5k}$ $r = \dfrac{-15k - 3}{5k}$